AWhat changed
Householder uses successive orthogonal reflections to triangularize a real matrix while preserving Euclidean geometry, reducing the square-root count compared with a sequence of plane rotations.
Scientific scope
Householder uses successive orthogonal reflections to triangularize a real matrix while preserving Euclidean geometry, reducing the square-root count compared with a sequence of plane rotations. The admitted algorithm is real orthogonal-reflection triangularization, particularly for nonsingular inversion and full-column-rank least squares. Zero/aligned columns need lawful skip/identity branches. The original arbitrary-complex lemma omits a needed phase condition and is not adopted here; later phase-aware repair is separate. Exact norm preservation is not blanket floating-point stability or a universal ill-conditioned pseudoinverse solution.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Alston S. Householder · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Alston S. Householder, Unitary Triangularization of a Nonsymmetric Matrix (1958), original article hosted by Stanford
- MIT Journal of the ACM bibliography: David D. Morrison, Remarks on the Unitary Triangularization of a Nonsymmetric Matrix (1960)
- Stanford-hosted Trefethen classic numerical-paper list and 1993 course account
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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